69. Sqrt(x)

• Difficulty: Easy

• Topics: Math, Binary Search

• Similar Questions:

  • Pow(x, n)

  • Valid Perfect Square

Problem:

Implement int sqrt(int x).

Compute and return the square root of x, where x is guaranteed to be a non-negative integer.

Since the return type is an integer, the decimal digits are truncated and only the integer part of the result is returned.

Example 1:

Input: 4
Output: 2

Example 2:

Input: 8
Output: 2
Explanation: The square root of 8 is 2.82842..., and since 
             the decimal part is truncated, 2 is returned.

Solutions:

class Solution {
public:
    int mySqrt(int x) {
        int left = 0;
        int right = INT_MAX;
        while (left + 1 < right) {
            int mid = left + (right - left)/2;
            if (x/mid >= mid) { // mid * mid <= x would cause overflow
                left = mid;
            } else {
                right = mid;
            }
        }

        if (x/right >= right)   return right;
        return left;
    }
};